Heat flux volumetric

Under normal operating conditions the first wall must handle high plasma surface heat fluxes (Table 1), as well as volumetric heat loadings due to the penetrating neutron and electromagnetic radiation. The volumetric heat loading is dependent... 

Volumetric heat release rates The rates of volumetric heat release from shell boiler furnaces fired by oil and gas are typically 175,000 to 235,000 Btu/ft3/hr. (Heat releases from the various tube passes are significantly lower than from the furnace, thus reducing the overall heat-flux rating.)... 

The second reason for high rates of heat transfer is that the volumetric particle heat capacity is about 1000 times greater than that of a gas and therefore approximates to that of a liquid. As Botterill (1975) has pointed out, a fluidized bed is effectively a fluid of high heat capacity but very low vapour pressure. Third, the very high specific surface of the particles results in high heat fluxes. 

Consider a tube heated uniformly at a heat flux q/A fed with saturated water at the base at a velocity Fo. For this velocity and heat flux, nucleate boiling will take place, and a temperature difference aTo will be established. At some distance up the tube vaporization will occur and increase the volumetric flow of material and hence the velocity to, say, Fi. The line for forced convective heat transfer meets the boiling curve below the heat flux of q/A and so nucleate boiling will still be the mode of heat transfer and the temperature difference AT, and hence the heat transfer... 

If we neglect the thermal energy spent on heating the reacting mixture itself, then all the heat of reaction is carried away by thermal conduction, and we must equate the heat flux to the overall amount of heat released in the flame per unit time, i.e., to the product of the volumetric heat capacity of the mixture, pQ, and the flame velocity ... 

Conduction with Heat Source Application of the law of conservation of energy to a one-dimensional solid, with the heat flux given by (5-1) and volumetric source term S (W/m3), results in the following equations for steady-state conduction in a flat plate of thickness 2R (b = 1), a cylinder of diameter 2R (b = 2), and a sphere of diameter 2R (b = 3). The parameter b is a measure of the curvature. The thermal conductivity is constant, and there is convection at the surface, with heat-transfer coefficient h and fluid temperature I. ... 

Application of the law of conservation of energy to a three-dimensional solid, with the heat flux given by (5-1) and volumetric source term S (W/m3), results in the following equation for unsteady-state conduction in rectangular coordinates. 

Soil has a substantial volumetric heat capacity, but it does not have a high thermal conductivity coefficient, Ks°l1. Heat is therefore not readily conducted in soil, where the heat flux density by conduction is... 

In Eqs. (6) and (7) e represents the internal energy per unit mas, q the heat flux vector due to molecular transport, Sh the volumetric heat production rate, ta, the mass fraction of species i, Ji the mass flux vector of species i due to molecular transport, and 5, the net production rate of species i per unit volume. In many chemical engineering applications the viscous dissipation term (—t Vm) appearing in Eq. (6) can safely be neglected. For closure of the above set of equations, an equation of state for the density p and constitutive equations for the viscous stress tensor r, the heat flux vector q, and the mass flux vector 7, are required. In the absence of detailed knowledge on the true rheology of the fluid, Newtonian behavior is often assumed. Thus, for t the following expression is used ... 

Also provided by the finite element solver is the source term SQ in the energy balance, eqn. (6). Except within the H2 release zone, the volumetric heat flux corresponds to heat losses by Joule effect in the conducting materials. In zone , the heat dissipated by the irreversible interfacial processes is computed instead. 

The symbols are defined as follows e is porosity p is gas density u is gas velocity t is time Cg is specific heat of the gas T is temperature of the gas x is distance Vj, Vi, Cgi, Wi, hi, and Wi are the mass fraction, diffusion velocity, specific heat, molar rate of production, molar enthalpy, and molecular mass of species i, respectively kg is gas thermal conductivity ) is the thermal disperse coefficient /i is the volumetric heat-transfer coefficient between the porous medium and the gas T, Cg, and kg are the temperature, specific heat, and thermal conductivity of the porous medium, respectively and q is the radiative heat flux in the x-direction. 

Where v is the volumetric growth rate of the bubble (calculable from the heat flux). The time required for the formation of a new macrolayer with its associated vapor mushroom was very short and the frequency of vapor mushroom departure is therefore f 1/x. 

Typical heat transfer results to monodisperse sprays impacting on a heated surface are shown in Fig. 18.24. The liquid flow rate is varied over a wide range, while the droplet diameter is kept almost constant [136]. The heat flux versus surface temperature trends are similar to those of conventional boiling curves (see Chap. 15 of this handbook), and the heat fluxes are very high. The available experimental data [133, 134,137-140] show that the volumetric spray flux V (m3/m2 s) is a dominant parameter affecting heat transfer. However, mean drop diameter and mean drop velocity and water temperature have been found to have an effect on heat transfer and transitions between regimes. Urbanovich et al. [141], for example, showed that heat transfer is not only a function of the volumetric spray flux but also of the pressure difference at the nozzle and the location within the spray field (Fig. 18.25). 

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